You only get the bonuses (both the extra attack dice and the bonus to the effect die) for the attack in which the tokens are removed. Just the one attack roll. This actually doesn’t have to be the first attack though, since removing the tokens to activate the ability is optional.

I think this is the relevant part of the staff of storms text that I missed when we discussed this previously

Quote

When making a Wind or Lightning attack, during the roll dice step you may remove any number of storm tokens to roll 1 additional attack die and gain +1 to the effect roll per token removed

If it weren't for the "during the roll dice step" part, I would argue that this acts just like the ring of tides and affects each roll. Unfortunately, I think the above stops that from happening, much to my disappointment.

You only get the bonuses (both the extra attack dice and the bonus to the effect die) for the attack in which the tokens are removed. Just the one attack roll. This actually doesn’t have to be the first attack though, since removing the tokens to activate the ability is optional.

Does this mean that you could remove one in the Roll Dice step of the Chain Lightning's first attack, and then another for the Roll Dice step of the second attack and so on?

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"Frost damage is a scam an armor dealer invented once to make a Beastmaster buy a new fur" - Exid

Does this mean that you could remove one in the Roll Dice step of the Chain Lightning's first attack, and then another for the Roll Dice step of the second attack and so on?

Absolutely. I feel obligated to remind people though that it has been ruled for Chain Lightning that any modifiers to the attack dice of one Chain Lightning attack do not carry over or affect subsequent attacks. I assume everyone already knows this, but thought I'd mention it just in case. This is covered in detail in the supplement.